Project Scheduling Diagrams: Gantt, CPM, PERT, and Inventory Control

Saw-Tooth Diagram for Inventory Management

The Saw-Tooth Diagram is a design used for input control and monitoring of stock. This graph serves to manage inventories, ordering, and the volume of flow itself.

The optimal quantity is determined according to the purchase price, storage costs, and handling volume. The optimal lot (often related to the Economic Order Quantity or EOQ, here referred to as PDID) includes the purchase price, carrying costs, PDID costs, overhead costs, and costs incurred until the item reaches the point of sale or placement.

Henry Gantt and the Gantt Chart

Henry Gantt was an American engineer belonging to the classical school of organization who planned American military transport during World War I, using bar-line graphs.

The Gantt Chart relates two sets of information: work units and the duration of the work. This graph is also called a calendar of events, determining the start and termination of each duration.

Gantt Chart Representation

• The X-axis represents totally ordered time.
• The Y-axis (ordinate) represents the whole work divided into activities, usually categorized into classes.

To utilize the Gantt Chart effectively, we need to know the duration of the activities, the available resources, and their performance.

Linked Gantt Charts and Schedule Control

The Gantt chart offers many possibilities for schedule control. Within the graph, it is possible to:

• Establish fields for cumulative values.
• Periodically monitor compliance with planning on a given day by noting the extent of completion for each item.
• Establish branches within the classes of items.

Network-Based Systems (CPM and PERT)

Network-based graphs belong to a graphical representation where networks represent sets that are not totally ordered. These graphs are based on numerous elements and their mutual dependence. The resulting systems are related to the critical path methods, such as CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique).

Key Elements of Arrow Network Diagrams

The elements that compose the arrow network diagram are:

• Activity: An activity (or sub-process into which a project is decomposed) consumes time and resources. It is represented by an arrow, has a unidirectional character, and possesses an origin and a final node (knot).
• Event (Suceso): The beginning or end of an activity. Events do not consume time or resources and are represented by circles (nodes).

Classification of Project Activities

Activities are classified depending on their distinct relationships:

1. Relationship with Events.
2. Relationship with other activities (Activities in series and activities in parallel).
3. Relationship with duration (Real and fictitious activities).

Rules for Constructing Arrow Network Diagrams

The construction of an arrow network follows specific rules:

Indicative Rules

• Use straight paths, avoiding crossings.
• Be proportional and avoid small angles.

Mandatory Rules

• Only indispensable fictitious activities are allowed.
• The network must have only one initial event and one final event.
• Two events joined by different activities cannot start simultaneously (i.e., two events cannot be connected by more than one activity unless a dummy activity is used).
• No loops or closed circuits are allowed.
• The transitive property must be satisfied.

Methods for Arrow Network Construction

There are several alternative methods for constructing an arrow network diagram:

1. Initial Event Method (Forward Pass): This involves assuming the activities and placing the initial event first. Subsequently, the final events of each activity are placed, and activities that share these initial events are successively connected until the final event is reached.
2. Final Event Method (Backward Pass): This involves traversing the previous process in the inverse sense, starting from the end and providing activities so that they are completed last.
3. Independent Method: This involves building a significant part of an activity both forward and backward simultaneously.